As explained in Ref. [1]},
one defines the MD evolution in fictitious time \(\tau \)  to be governed by a Hamiltonian
which receives contributions \(H_g\)  from gauge fields, and \(H_f^R\)  from each
species of fermions in representation \(R\)  of the group—see
Eqs. (15)-(18) in Ref. [1]}.
If we want to describe \(n^R\)  degenerate (Dirac) fermions in a given representation \(R\) ,
we need to be more precise in the definition of the pseudofermions
and how they enter the exponent in Eq. (REF ), and the Hamiltonian \(H_f^R\) .
We introduce \(N_{\rm pf}\)  pseudofermions \(\phi _k^{R}\)  and \(\phi _k^{R\,\dagger }\) ,
and their Hamiltonian is determined by the Dirac operator in the representation \(R\) :
\(H_f^R=\sum _{k=1}^{N_{\rm pf}}\sum _x\phi ^{R,\dagger }_k(x) \left(\left(Q_m^{R}\right)^2\right)^{-l_k}\phi ^R_k(x)\,,\) 
